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Aditya Math Practical 5

The document contains practical exercises using Scilab commands to analyze matrices, including finding dimensions, norms, orthogonal bases, kernels, and ranks. Multiple matrices are defined, and their properties are calculated, such as vector lengths and orthogonality. The results of these calculations are presented for each matrix in a structured format.

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52 views9 pages

Aditya Math Practical 5

The document contains practical exercises using Scilab commands to analyze matrices, including finding dimensions, norms, orthogonal bases, kernels, and ranks. Multiple matrices are defined, and their properties are calculated, such as vector lengths and orthogonality. The results of these calculations are presented for each matrix in a structured format.

Uploaded by

kayyummulani333
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Name- Suryawanshi Aditya

Roll no- 64

Practical-05
Q1) Find dimensions matrix as vector space
using scilab command and also find vector
length.

a=[1 2 -3 4;0 1 -2 4;-3 2 1 1;]

a = [3x4 double]

1. 2. -3. 4.

0. 1. -2. 4.

-3. 2. 1. 1.

--> b=[9 -3 0 1 2;3 4 -2 1 0;4 -5 1 -2 3;]

b = [3x5 double]

9. -3. 0. 1. 2.

3. 4. -2. 1. 0.

4. -5. 1. -2. 3.

--> c=[1 1 1;0 1 1;0 1 1;]


c = [3x3 double]

1. 1. 1.

0. 1. 1.

0. 1. 1.

--> d=[6 2 1;-1 2 4;5 4 5;4 6 9;]

d = [4x3 double]

6. 2. 1.

-1. 2. 4.

5. 4. 5.

4. 6. 9.

--> norm(a)

ans =

7.0987731

--> norm(b)

ans =

11.571832
--> norm(c)

ans =

2.5243378

--> norm(d)

ans =

15.067379

--> size(a)

ans = [1x2 double]

3. 4.

--> size(b)

ans = [1x2 double]

3. 5.

--> size(c)

ans = [1x2 double]


3. 3.

--> size(d)

ans = [1x2 double]

4. 3.

Q2) Find orthogonal basis using scilab


command.

--> a=[1 2 -3 4;7 3 2 0;2 -3 0 1;]

a = [3x4 double]

1. 2. -3. 4.

7. 3. 2. 0.

2. -3. 0. 1.

--> b=[4 -3 1 2;-2 1 0 1;1 2 -1 3;]

b = [3x4 double]

4. -3. 1. 2.

-2. 1. 0. 1.

1. 2. -1. 3.
--> c=[1 4 5 2;2 1 3 0;-1 3 2 2;]

c = [3x4 double]

1. 4. 5. 2.

2. 1. 3. 0.

-1. 3. 2. 2.

--> orth(a)

ans = [3x3 double]

-0.2010075 -0.9785058 -0.0460691

-0.9747174 0.1951017 0.1089099

-0.0975808 0.066796 -0.9929835

--> orth(b)

ans = [3x3 double]

-0.9474389 -0.0117435 0.3197211

0.3017191 0.2996056 0.9050978

-0.1064193 0.9539909 -0.2803148

--> orth(c)

ans = [3x2 double]


-0.8151481 0.0469068

-0.3669516 0.7293923

-0.4481965 -0.6824856

--> a=[1 -4 7;-8 7 6;4 1 0;]

Q3) Find kernel (null space) of the following


and also find rank of matrices.
a = [3x3 double]

1. -4. 7.

-8. 7. 6.

4. 1. 0.

--> b=[3 1 -7 6;4 2 1 -4;-3 2 -1 9;]

b = [3x4 double]

3. 1. -7. 6.

4. 2. 1. -4.

-3. 2. -1. 9.

--> c=[-1 2 4 7 3;1 2 4 -8 9;-7 4 6 7 3;]


c = [3x5 double]

-1. 2. 4. 7. 3.

1. 2. 4. -8. 9.

-7. 4. 6. 7. 3.

--> d=[4 -3 1 2;1 -2 -4 -5;-9 -6 -1 8;]

d = [3x4 double]

4. -3. 1. 2.

1. -2. -4. -5.

-9. -6. -1. 8.

--> kerel(a)

Undefined variable: kerel

--> kernel(a)

ans =

[]

--> kernel(b)

ans = [4x1 double]


-0.5469214

0.5938962

-0.4630377

-0.3657327

--> kernel(c)

ans = [5x2 double]

-0.3505075 0.0558265

-0.5161789 0.7747506

-0.5353436 -0.6072711

0.1705322 0.0683611

0.5431664 0.152294

--> kernel(d)

ans = [4x1 double]

0.2440588

0.3995652

-0.7408156

0.4816381

--> rank(a)

ans =
3.

--> rank(b)

ans =

3.

--> rank(c)

ans =

3.

--> rank(d)

ans =

3.

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